Resonant Quantum Hydrodynamics of Solid-State Topochemical Reactions in Constrained Nanocrystalline Lattices: A Convergent Field-Theoretic Framework

Abstract

We formulate a continuum and field-theoretic paradigm in which solid-state topochemical reactions confined within nanocrystalline lattices are modeled as coherent quantum-hydrodynamic systems. Traditional chemical kinetics, bounded by the classical Arrhenius activation energy barrier and chaotic thermal molecular collisions, fail to explain or optimize macro-level synthesis under strong spatial constraints. We propose a convergent framework expanding classical reaction-diffusion systems, specifically the Kolmogorov-Petrovsky-Piskunov and Allen-Cahn equations, into non-Euclidean state spaces coupled self-consistently with the Schrödinger-Maxwell equations. By analyzing the electron density wave-function dynamics under external magnetic and laser resonances, we demonstrate that electron hybridization clouds achieve non-local, synchronous tunneling transitions across regularized crystal barriers without thermal dissipation. The boundary operator is verified numerically using a Fast Fourier Transform regularization of the boundary profile and unfolded level-spacing statistics matched against the Gaussian Unitary Ensemble (GUE) Wigner surmise. Finally, we provide a formal Lean 4 architecture checkable loop of the topochemical constraints consistency and a detailed engineering analysis of its practical implications for targeted drug manufacturing and advanced aerospace materials.